Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 4x - 3$ and $ KL = 2x + 9$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {4x - 3} = {2x + 9}$ Solve for $x$ $ 2x = 12$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 4({6}) - 3$ $ KL = 2({6}) + 9$ $ JK = 24 - 3$ $ KL = 12 + 9$ $ JK = 21$ $ KL = 21$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {21} + {21}$ $ JL = 42$